So, you have a bunch of Nations, Kingdoms and Countries all set up for your world. Let's see how they can interact with each other. There are a number of ways that nations can view each other, and their relationships can be as complex as those between characters. So let's examine a few kinds of international relations
Close allies: This is about as good as it gets, these nations are tied very neatly together. They likely share a great deal of trade, have frequent exchanges of citizens, ideas, and technologies. As a result it's very common for closely allied nations to slowly blend their cultures and religions, though this is not always the case. Since most nations tend to be pragmatic by necessity, close allies are usually formed between bordering countries. Often times close allies will experience mergers over times, but this is definitely not always the case. Often times even the closest of allies are happy to celebrate their differences and even use those differences as a fundamental part of cultural identity. And of course if a closely allied country goes to war then it's only natural to provide support by whatever means are possible. A good example of close allied nations would be Canada and the United states of America. Well, it would be as of a year or two ago anyways.
Allies: Allied nations share trade, travel, and often times international laws. An ally nation is best marked by civil agreements to uphold certain universal beliefs that all allies can agree upon. These are usually laws that regulate how one nation treats the world, and treats the people in that world. An allied nation in a fantasy game might be another country that also hates the undead and views them as a menace, or might be a fellow kingdom that forbids wild magic. Allies are bound together by agreements, and by a mutual benefit, usually relying on trade to form that foundation. An ally is a fellow nation that plays by the same rules, and if they go to war then you must strongly consider joining them. A good example being the United Kingdom and France, despite some personal differences, they both are members of the united nations, and often both fall into similar views on various accords regarding war crimes and environmental concerns.
Neutral: A Neutral relationship among nations generally comes between two far removed countries that don't rely on each other for much. This commonly occurs between two distant countries, particularly ones that don't deal a great deal in trade. A Neutral nation is by no means an enemy, and can still engage in trade of course, but they both agree to live and let live and to pursue their own goals quite separate of each other. A neutral country is unlikely to get involved in the wars of it's other neutral countries. Switzerland has a reputation for maintaining neutrality to a legendary extent.
Hostile: A Hostile nation is a country that carries on unacceptable practises within its borders. It's a country that conducts itself in a way that is morally reprehensible, a country that must be changed for the better, preferably by diplomatic means. In a near future world where cloning is abolished, a country that instead churns out and enslaves clones of its citizens may quickly find itself branded as a hostile nation. So too might a fantasy or superhero kingdom ruled by the use of powerful mind control. Hostile nations are the frequent targets of bans, sanctions, exclusion, trade tariffs, and military posturing and veiled threats. All of these ideas are meant to force another country to change, without resorting to war. These countries are also the most prone to covert operations, the use of spies, cyber attacks, election tampering, and the blackmail of top political figures. A good example of this would be the United states and Russia.
Cold war: This is the step above hostile, open aggression, direct military posturing and threats. A cold war is the last desperate phase before a full war. Hostile nations are not changing and they are not backing down. Aggressions have reached a boiling point. At this point countries will form embargos, blockades, travel bans and other offensive economic actions. It's also common for the nations at cold war to push their allies and other neutral countries to take the same, requesting or demanding that stances be taken and battle lines be drawn. Countries in cold war are filled with tension, and any day they could find themselves battling to the death even while spies have been infiltrating and covert ops have been taking place for months or years already. Cold war is perhaps the hardest of these categories to identify, though "The Cold War" between Russia and United states springs to mind as a good example.
War: The ultimate failure of diplomacy. War is one of the worst things a nation can do to another. To use ones most terrible weapons and tactics on another group with the express purpose of harming them. War is devastating economically, socially, spiritually, mentally and physically. It causes damage to buildings, crops, animals, soldiers and innocents alike with little to no discretion or distinction. Countries at war almost invariably drag their allies into it, and thusly spread even more destruction and damage until either one side "wins" by outlasting the other, or until all involved are so weakened and weary and wounded that they agree to a peaceful resolution. If you need an example of a country being at war, just look at the history of any country ever.
Of course there are likely to be some outside cases where the lines between the above are blurred. International politics can be a lot more complicated than this, but let these categories serve as a good starting point for you.